1. Charlotte was worried about the hygiene of a new restaurant at her university, and she would like to use difference equations to model the population
growth of cockroaches inside the kitchen of that restaurant. She assumed that
there was one pair of cockroach larvae (i. c. baby cockroach), one of cach gender,
and one pair of matured cockroaches, one of cach gender, in the kitchen at the
beginning of October 2018. She checked that all cockroach larvae mature into
adulthood in one month, after which a couple of matured cockroaches would
produce 42 pairs (with equal number in cach gender) of cockroach larvae every
month. That means, at the beginning of December 2018, the mentioned pair of
cockroach larvae would have turned into adult and started reproducing, while
the mentioned one pair of adult cockroaches would have reproduced once by the
beginning of November 2018 and would keep on reproducing in the subsequent
months. Assuming that all the cockroaches in the kitchen would not die and
the kitchen has always been isolated from the outside world, how many pairs
of cockroaches (adult cockroaches as well as larvae) will there be approximately
(correct to 3 significant figures) in the kitchen at the beginning of September
20217
(A) 1.43 x 10
(B) 1.64 x 1030
(C) 6.12 x 1080
(D) 6.16 x 10%
(E) 1.14 x 1041
(F) 8.01 x 1051
(G) None of the above